In this section we illustrate our approach in the context of a concrete new-physics scenario, which has been proposed to address some of the \(B\) -meson anomalies observed in the transitions \(b\rightarrow s\mu ^+\mu ^-\)  [1]}. The setup we consider is an extension of the SM with a gauged \(L_\mu -L_\tau \)  lepton number, denoted by \(U(1)^{\prime }\) . The new symmetry is broken spontaneously by the VEV \(\langle S\rangle \equiv u/\sqrt{2}\)  of a complex scalar field \(S\) , which is charged under the \(U(1)^{\prime }\)  with \(Q_S^{\prime }=1\)  and transforms as a singlet under the SM gauge group. The associated gauge boson \(Z^{\prime }\)  acquires a mass \(m_{Z^{\prime }}=g_{Z^{\prime }}{\hspace{0.85358pt}}u\) , where \(g_{Z^{\prime }}\)  is the gauge coupling of the \(U(1)^{\prime }\)  and we assume that \(u\gg v\) . The muon and tau lepton carry charges \(+1\)  and \(-1\)  under the \(U(1)^{\prime }\) , whereas the remaining SM fermions are uncharged.
